The scale factor for two similar rectangles is 9. If the area of the smaller rectangle is 3cm^2, what is the area of the larger rectangle?
Responses
729 cm^2
243 cm^2
81 cm^2
27 cm^2
The scale factor for the two similar rectangles is 9, meaning that each corresponding linear dimension of the larger rectangle is 9 times that of the smaller rectangle.
When dealing with similar figures, the areas are proportional to the square of the scale factor. Thus, if the scale factor for the linear dimensions is 9, the scale factor for the areas will be 9^2 = 81.
To find the area of the larger rectangle, we multiply the area of the smaller rectangle by the area scale factor:
Area of larger rectangle = Area of smaller rectangle × (Scale factor)^2
Area of larger rectangle = 3 cm^2 × 81
Area of larger rectangle = 243 cm^2
Therefore, the area of the larger rectangle is 243 cm^2.